Brexit wrecks it: the theory of collective decision making

Basically, political decision-making should not be win-or-lose, as facilitated by the most ancient, primitive, divisive and inaccurate measure of collective opinion ever invented.

The people have spoken? No no, at 52-48, they have
disagreed. Some referendums are OK, like the Belfast Agreement; others are
dodgy; a few, as in the Balkans, provoked wars.

Logically, the will of the people cannot be identified if
lots of them state only what they do not
want. However, if the choice of options is sufficiently broad so that folks can
vote positively, we may identify the will of a majority (or maybe just the largest
minority). Better still, if they cast their preferences, we can identify the
option most acceptable to (almost) everybody.

This article discusses decision-making and makes only
passing reference to elections. With regard to the 2011 referendum on the
electoral system and Brexit, it examines binary and multi-option voting; then,
going a little more technical, it shows that the collective will can be identified with preferential
voting.

Majority voting

Two-option questions may be necessary in law: guilty or not
guilty? In politics, however, topics like the electoral system or our
relationship with Europe need not be reduced to binary ballots: “option A
or B?”
or worse, “A, yes or no?”

Indeed, there may be only one political question where a
binary choice summed up the entire debate: “Which side of the road shall we
drive on?” Even then, in Sweden’s 1955 referendum, there were three options on the ballot paper:
‘left’, ‘right’ and ‘blank’. So those indifferent could also vote, choosing
‘blank’ and thus supporting the winning option; everyone was able to vote
positively.

Basically, political questions should not be closed
dichotomies: “Are you Protestant or Catholic? Serb or Croat? communist or
capitalist? for or against?” Decision-making should not be win-or-lose, as facilitated
by the most ancient, primitive, divisive and inaccurate measure of collective
opinion ever invented.

Unfortunately, politicians like to control things. In 2011,
David Cameron decided that a referendum would be “A v B ”: first-past-the-post, (fptp), versus the alternative vote, (av). For supporters of proportional representation (pr), that’s like asking a vegetarian,
“beef or lamb?” When New Zealand debated electoral reform, an independent
commission drew up a short list of five options, from fptp to the Irish form of av,
proportional representation, single transferable vote (STV), pr-stv. So (nearly) everyone could vote positively and New
Zealand, like Germany, now has half fptp
and half pr-list.

There were at least four options on Brexit: A,
the EU; B the EEA; C the Customs Union and D,
the WTO, but Mr Cameron decided this vote would be, in effect, “A,
yes-or-no?” So B, C and D supporters voted ‘no’ – or ‘leave’.
If the question had been “B, or C, or D,
yes-or-no?” doubtless the answer would also have been a majority ‘no’. To state,
then, that this ‘remain-or-leave’ ballot identified the will of the people is
as illogical as to claim, on the basis of the 2011 referendum, that the British
people prefer fptp to pr.

Multi-option voting

If the choice is binary, a (simple or weighted) majority
vote is the only appropriate methodology. But in politics, as noted, complex
questions should not be reduced to two options. Moreover, no one individual
should be able to dictate the referendum question, (as did Napoleon, Hitler et al).

If there are three or more options, several decision-making
procedures are available. They include plurality voting; the two-round system, (trs); av; and a points system.

Plurality voting is like the UK’s fptp; voters choose just one option from a ‘plurality’ of them,
and the option with the most votes wins.

With trs, the
French electoral system, if nothing wins 50%+ in the first round plurality
vote, a second round majority vote is held between the two leading options.

av is used in Australian elections,
while pr-stv is popular in
Ireland. In a series of plurality votes, the least popular option is eliminated
and its votes transferred as per its voters’ wishes… until one option wins a majority.

The modified Borda count, (mbc),
is a points system. With four options, a 1st preference may get 4
points, a 2nd 3, a 3rd 2, a 4th 1… and the
option with the most points wins. The bc
is used in Slovenian elections and, a slightly different version, in Nauru.

Consider, then, Table I, a voters’ profile in which 14 voters
cast their preferences on options E, F, G and H.
Option E is obviously very polarised, F is
also divisive, G is a bit better, but it seems H best
represents the consensus.

Table I A Voters’ Profile

Preferences

Number of voters

5

4

3

2

1st

E

F

G

H

2nd

H

H

H

G

3rd

G

G

F

F

4th

F

E

E

E

Plurality voting counts only the 1st preferences,
so the social ranking is E 5, F 4, G 3, H 2, and the social
choice is E.

So the democratic choice is E, or F,
or G,
or H.
But, as suspected above, option H best represents the collective will.
With this particular profile then, as with many others, the ‘alternative’
outcomes of E, F and G are ‘post-truth’ popularities, to
quote current jargon. Likewise, the (almost binary) US presidential contest meant
that Donald Trump’s victory was ‘fake’.

Preferential voting

Of the above methodologies, only the mbc counts all the preferences of all the voters. Little
wonder, it is the most accurate, (as is the Condorcet criterion). At best, the mbc identifies the option with the
highest average preference, and an average of course involves not just a
majority but every voter; the mbc
is win-win.

Moreover, as long as the options are finalised independently, it
best qualifies under Kenneth Arrow’s ‘impossibility theorem’. Indeed, according
to Sir Michael Dummett, it “is the soundest method of identifying the… most
acceptable” option, while Don Saari concludes, “only [it] offers an accurate
accounting of the voters’ preferences.”

Let’s take the argument further. If the Brexit options – (A)
EU, (B)
EEA, (C) Customs Union and (D) WTO – are listed in order ‘soft’
to ‘hard’, then the voters’ preferences may follow a pattern. If Mr i's 1st
preference is D, he may have a 2nd of C, a 3rd of B
and a 4th of A. Similarly, Ms j and Ms k, whose favourite
is B,
may have a 2nd preference of A or C, a 3rd of C
or A,
and a 4th of D.

Table II Single-peaked Preferences

Table II shows that these sets of preferences are all
‘single-peaked’. If Mr l, however, has preferences of 1st C,
2nd A, 3rd D and 4th B, his
set, suitably dotted, will have two peaks, as in Table III.

Table III An Oddity

If the voters do cast single-peaked preferences, the points totals
will also be single-peaked. The peak of this collective set, as in Table IV, is
the “will of the people”. Furthermore, the sheerer the summit, the greater the
degree of consensus. It is an exact science.

Consensus decision making

an independent authority shall draw up the final
(short) list of options;

those concerned shall cast (one, some, or all)
their preferences; and

if the option with the most points passes a
pre-determined threshold, it shall be enacted.

The current scenario

The outcome of the Brexit vote was at best unclear. Any
future binary referendum like the Lib-Dem proposal would be equally vague and
could lead to a never-end-’em. Similarly,
in any binary parliamentary vote, “mps
would have a choice between only [Mrs May’s] terms and no deal at all,” so, to
quote Gus O’Donnell, (The Guardian,
21 February), it would “amount to nothing.”

The danger, of course, is that the world’s obsession with
majority voting/rule will continue; that Le Pen, Wilders etc. will dictate
their own referendum questions; and that the forces of populism will continue
to vote ‘no’… to everything… until there is nothing.

About the author

Peter Emerson, the child of an English Catholic mother and Irish Protestant father, is the director of the de Borda Institute, a Belfast-based NGO which specialises in voting systems for decision-making. He has worked in several other conflict zones as well, in the Balkans, the Caucasus and East Africa. His latest book is From Majority Rule to Inclusive Politics, (Springer, 2016).

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